1. Field of the Invention
The present invention relates to a method for measuring the dead time of a pulse type X-ray detector.
2. Description of the Related Art
A pulse type X-ray detector, including for example a proportional counter, a scintillation counter and a solid-state detector such as an avalanche photo diode, can detect an X-ray intensity by counting the number of X-ray photons, i.e., particles. Accordingly, the pulse type X-ray detector has, in principle, the disadvantage of counting loss based on the finite dead time. When two X-ray photons enter the pulse type X-ray detector with a time interval smaller than the predetermined time, the two X-ray photons can not be observed separately but would be counted as one or less X-ray photon. The predetermined time described above has been referred to as the dead time. The dead time consists of a time inherent in a detecting device and another time comes from an electronic circuit such as a pulse height analyzer. The present application aims the dead time as viewed from the final output of the X-ray detector, i.e., the dead time in total of the X-ray detector.
There will now be explained a corrected expression of an X-ray detection intensity in consideration of the dead time. Equation (1) in FIG. 1 is a corrected expression of an X-ray detection intensity in an asphyxiant type X-ray detector which uses an amplifier. In equation (1), Iobs indicates an X-ray intensity actually observed in the X-ray detector, Itru indicates a true X-ray intensity having entered the X-ray detector, and τ indicates the dead time. The unit of an X-ray intensity is the count number per unit of time, cps for example. FIG. 2 shows a graph of equation (1), Itru in abscissa and Iobs in ordinate. A straight broken line 10 indicates that Iobs is equal to Itru, this is the ideal state without counting loss, which means that the dead time is zero. When with the finite dead time τ, the shape of equation (1) becomes a mound curve, Iobs becoming maximum when Itru is equal to 1/τ.
Equation (1) can be transformed so that Itru comes to the left side, resulting in equation (2) in FIG. 1. This equation (2) is used to obtain a true X-ray intensity Itru with the use of an observed X-ray intensity Iobs and the dead time τ. The nested structure of exp in equation (2) continues infinitely. In an actual calculation, however, the number of nesting may be cut off at the predetermined number. If the predetermined number is large enough, a true X-ray intensity is obtained with a sufficient accuracy. Equation (3) indicates an approximate equation in which the number of nesting is cut off at three.
FIG. 3 shows a graph indicating a variation of a calculated quantity of equation (2), i.e., a calculated true X-ray intensity Itru, with the number of nesting, provided that the calculation is carried out with two hundred thousand cps in observed X-ray intensity Iobs and 8×10−7 seconds in dead time τ. When the number of nesting is increased, the calculated quantity is convergent. As clearly seen from FIG. 3, about ten nesting would be sufficient because the good calculation result is obtained at ten nesting almost the same as that with the infinite nesting.
Therefore, if the number of nesting is large enough, a true X-ray intensity Itru can be determined with a sufficient accuracy based on equation (2) with the use of an observed X-ray intensity Iobs and the dead time τ.
If the dead time τ is known, a true X-ray intensity can be calculated with an observed X-ray intensity Iobs as described. Then, it is important, in the counting loss correction, to determine the dead time τ precisely. The conventional methods for determining the dead time is disclosed in, for example, (1) Elements of X-ray Diffraction, Second Edition, written by B. D. Cullity, Japanese Version, translated by G. Matsumura, published by Agune (Japan), 1980, page 181 (which will be referred to as the first publication hereinafter) and (2) Experimental Physics Course 20, X-ray Diffraction, edited by K. Kohra, published by Kyoritsu Shuppan (Japan), 1988, pages 147-148 (which will be referred to as the second publication hereinafter).
The first publication discloses that (i) a plurality of metal foils having the same thickness are superimposed on one another to make an absorber, (ii) the absorber is inserted into the X-ray path, and (iii) X-ray intensities are detected with removing one metal foil after one detection. Plotting the number of the metal foils removed in abscissa while observed X-ray intensities (cps) in ordinate having a logarithmic scale, the logarithmic observed X-ray intensities are proportional to the removed numbers in a range of the smaller number of the removed metal foils, that is, in a range in which X-ray intensities are weak and thus there is almost no counting loss. On the other hand, when the removed number becomes larger, that is, in a range in which X-ray intensities become stronger and thus the counting loss is increased, the logarithmic observed X-ray intensities are out of proportional to the removed numbers. Taking account of such a plotted graph, it is understood how much X-ray intensity raises considerable counting loss. Extending the proportional relationship which is derived in the smaller X-ray intensity range, a true X-ray intensity may be estimated even in the larger X-ray intensity range. It would be possible to determine the dead time, based on equation (1), with the estimated true X-ray intensity and the observed X-ray intensity.
There has been known another method using the tube current of an X-ray tube, instead of using the number of the metal foils, to vary an X-ray intensity. The X-ray intensity of an X-ray tube is proportional to the tube current. Therefore, the dead time can be determined in a manner that (i) an X-ray intensity is detected with a small tube current, the observed X-ray intensity being almost equal to the true X-ray intensity, (ii) another X-ray intensity is detected with a large tube current enough to raise the counting loss, (iii) a true X-ray intensity with the large tube current is estimated based on the proportional relationship between the tube current and the true X-ray intensity and (iv) the dead time is determined using the estimated true X-ray intensity and the observed X-ray intensity.
Furthermore, the second publication introduces, as a method for determining the dead time experimentally, two books regarding the two-source method.
It is required, in the conventional methods, to estimate a true X-ray intensity by any means to determine the dead time experimentally. If the true X-ray intensity is determined based on the tube current as described above, there would occur problems described below. First, it takes about thirty minutes until the X-ray intensity becomes stable after change of the tube current. Further, it is not necessarily assured that an X-ray intensity entering the X-ray detector is actually proportional to the tube current. For example, since the change of the tube current raises the change of the focus position on the target, an X-ray intensity arriving at the X-ray detector is not necessarily proportional to the tube current. Especially, when an optical device such as a multilayer mirror is inserted between the X-ray source and the X-ray detector, an X-ray intensity entering the X-ray detector is definitely out of proportional to the tube current. Furthermore, it is necessary, for estimating a true X-ray intensity, to use an observed X-ray intensity which is obtained with a small tube current, and accordingly the resultant estimated high X-ray intensity would have a poor accuracy.
Even not using the tube current, as long as the dead time is determined based on the estimation of the true X-ray intensity by any means, the accuracy in determination of the dead time would depend on the accuracy in estimation of the true X-ray intensity.